Abstract

InAs/GaAs heterostructures have been simultaneously grown by molecular beam epitaxy
on GaAs (100), GaAs (100) with a 2° misorientation angle towards [01−1], and GaAs
(n11)B (n = 9, 7, 5) substrates. While the substrate misorientation angle increased from 0°
to 15.8°, a clear evolution from quantum dots to quantum well was evident by the surface
morphology, the photoluminescence, and the time-resolved photoluminescence, respectively.
This evolution revealed an increased critical thickness and a delayed formation of
InAs quantum dots as the surface orientation departed from GaAs (100), which was explained
by the thermal-equilibrium model due to the less efficient of strain relaxation on
misoriented substrate surfaces.

Keywords:

Introduction

Self-assembled InGaAs/GaAs semiconductor quantum dots (QDs) attracted extensive research
efforts due to their unique properties as “artificial atoms” [1-3]. Understanding and controlling the growth of InGaAs/GaAs QDs were important both
for fundamental studies and in view of their potential in optoelectronic device applications.
In this arena, it is well known that the GaAs substrate orientation has a large impact
on the formation and properties of the self-assembled InGaAs QDs [4-8]. This is due to the different oriented substrate surfaces that are characterized
by different chemical potentials thus affecting the kinetics of adsorption, migration,
desorption, reconstruction, and strain relaxation [9-12]. These differences, in turn, introduce new optical properties and potential applications
[13-16].

To date, there are many experimental and theoretical studies on the influence of GaAs
substrate orientation on the QDs. However, the formation and evolution of QDs on misoriented
substrates remain an interesting topic because they provide insight for designing
a QD device system [17]. Previously, Henini’s group developed the thermal-equilibrium model [18] and theoretically proved that the critical thickness of forming InAs QDs on high
index surfaces increased as the substrate orientation departed from the GaAs (100)
[19]. This proof was reinforced experimentally on GaAs (511)B surface (substrate misorientation
of 15.8°) and GaAs (311)B surface (substrate misorientation of 25.2°) [19,20]. Nonetheless, our recent investigation of InAs QDs grown on patterned substrate showed
that, with the misorientation angle less than 15°, the InAs QDs prefer to nucleate
on the vicinal surface rather than on GaAs (100) [21,22]. In this case, it seems that the critical thickness of forming InAs QDs on the vicinal
surface is less than that on planar GaAs (100). Thereafter, one question appeared:
does the thermal-equilibrium model still work well for the substrates with misorientation
angle smaller than 15.8°? To verify this, InAs have been simultaneously deposited
on GaAs (100), GaAs (100) with a 2° misorientation angle towards [01−1] direction
and GaAs (n11)B (n = 9, 7, 5) substrates. From the atomic force microscope (AFM) characterization and
photoluminescence (PL) investigation, a clear evolution from QDs to quantum well (QW)
was observed while the substrate misorientation angle increased from 0° to 15.8°.
This evolution proved that the critical thickness increased as the substrate orientation
departed from the GaAs (100).

Experiments

The samples used in this investigation were grown by solid-source molecular beam epitaxy
(MBE) on GaAs (100), GaAs (100) with a 2° misorientation towards [01−1] and GaAs (n11)B (n = 9, 7, 5) substrates. As shown in Table 1, the substrate misorientation angle θ, increased from 0° to 2°, 8.9°, 11.4°, and
15.8°, respectively. For convenience, they were labeled samples A, B, C, D, and E.
The growth was carried out simultaneously on five substrates soldered on the same
molybdenum block side by side to guarantee identical growth conditions. After loading
the molybdenum block into the MBE growth chamber, the surface oxide was thermally
desorbed at 600 °C. Thereafter, a 0.5-μm-thick GaAs buffer layer was grown at 600
°C followed by a reduction of the substrate temperature to 530 °C for the growth of
1.6 monolayer (ML) of InAs. By in situ reflection high-energy electron diffraction,
the growth rate of InAs was deduced to be 0.013 ML/s and the QD formation was confirmed
on GaAs (100) surface. After 15 s of growth interruption, a 20 nm GaAs capping layer
was grown on top of the QDs layer before the substrate temperature was raised to 600
°C for the growth of an additional 80 nm of GaAs capping layer. Finally, an identical
InAs QD layer was again deposited at 530 °C on top of the GaAs for morphology characterization
by AFM. The PL measurements were performed in a variable temperature (10–300 K) closed-cycle
cryostat under the excitation of a continuous-wave YAG laser with an operated-wavelength
of 532 nm. The PL spectra were analyzed by a 0.5-m spectrometer and were detected
by a liquid nitrogen cooled CCD camera.

Results and Discussion

Illustrated in Fig. 1 are the AFM images and the histograms of QD height. Clearly, the surface morphology
strongly depended on the substrate orientation. As shown by Fig. 1a and b, for sample A grown on planar GaAs (100), two families of InAs QDs formed on the
GaAs (100) surface. The bigger QDs had a density of 5.2 × 109 cm−2, a lateral size of (80.0 ± 8.6) nm and an average height of (14.7 ± 1.0) nm. The
smaller QDs had a density of 4.0 × 108 cm−2, a lateral size of (57.2 ± 10.8) nm and an average height of (6.1 ± 2.5) nm. The
formation of two families of QDs was attributed to two growth mode transition onsets
at 1.45 and 1.59 ML of InAs coverage [23]. For sample B, as shown by Fig. 1c and d InAs QDs were also observed on the surface, but the QDs exhibited a single-modal
distribution with a density of 5.8 × 109 cm−2, a lateral size of (51.1 ± 6.4) nm and an average height of (8.8 ± 1.4) nm. When
the substrate misorientation angle increased to 8.9°, i.e., for the sample C grown
on GaAs (911)B, as shown in Fig. 1e and f, the obtained QDs still exhibited single-modal distribution, but with a low density
of 1.0 × 109 cm−2 and a small average height of (5.2 ± 1.7) nm. Clearly, the QDs on (911)B surface
were closer to the two-three dimensional (2D−3D) growth mode transition than the QDs
did on samples A and B. When the substrate misorientation angle further increased
to 11.4° and 15.8°, i.e., for samples D and E, as shown by the AFM images in Fig.
1g and h there were no QDs found. The InAs growth was still 2D growth and QW was formed on
each surface. In summary of the AFM images in Fig. 1, a continuous morphology evolution from QDs to QW was clearly observed while the
substrate misorientation angle increased from 0° to 15.8°.

Then low temperature (T = 10 K) PL spectra was measured to verify the substrate orientation dependence and
the results are given in Fig. 2a. Each PL spectrum, which was excited with a laser intensity of 0.3 W/cm2, was normalized to its maximum. For sample A, the broad PL band around 1.1 eV was
related to InAs QDs, which exhibited a bimodal distribution and agreed with the AFM
observation. The peak at 1.058 eV with a FWHM of 30 meV and the peak at 1.117 eV with
a FWHM of 59 meV were attributed to the big QDs and the small QDs, respectively. The
narrow peak at 1.436 eV originated from the wetting layer (WL). For sample B, the
PL signal showed one QD peak centered at 1.201 eV with a FWHM of 49 meV and one WL
peak centered at 1.432 eV with a FWHM of 12.6 meV. For sample C, similarly, the PL
spectrum showed one QD peak at 1.291 eV with a FWHM of 93 meV and a WL peak at 1.431
eV with a FWHM of 12.8 meV. However, its QD peak had a big blue-shift and less intensity.
It can be seen that, from sample A to C, as the density and size of QDs decreases,
their PL emission became less intense and blue-shifted. When the misorientation angle
further increased to 11.4° and 15.8°, as shown in Fig. 2 there was no QD PL peak observed. Only the QW PL was founded for samples C and D.
Therefore, the PL spectra in Fig. 2a also showed a clear evolution from QDs to QW while the substrate changed from GaAs
(100) to GaAs (511)B, which was coincident with the AFM observation in Fig. 1.

To further examine the optical properties, samples B, C and E were selected to measure
the temporal PL (TRPL) behaviors. The measured PL band positions were indicated by
the letters in Fig. 2a and the corresponding TRPL data were plotted in Fig. 2b. For sample B, its WL emission, as shown by the curve-a, had a decay time as short as 110 ps. This short decay time was due to the fast exciton
relaxation from the WL to the confined energy states of QDs. The QD PL band at 1.201
eV had a decay time of 1,450 ps as shown by the curve-b, which is a typical value for InAs QDs. For sample C, its QD peak at 1.291 eV was
characterized by a QD decay time of 1,320 ps as shown by curve-c. However, as shown by the curve-d its WL PL has a decay time of 280 ps, which is longer than the WL decay time obtained
from curve-a. This long WL decay time is likely due to the very low QD density on (911)B surface.
Consequently, only a small fraction of the photon-generated electron–hole pairs can
recombine through the islands, and most of them have to recombine through the WL [24]. Finally, for sample E, there are no QDs. The PL band at 1.446 eV was characterized
by a decay time of 640 ps, which means a typical QW characterization. The evolution
from QDs to QW was further proved by the TRPL measurement while the substrate orientation
changed from GaAs (100) to GaAs (511)B. Interestingly, in this investigation not only
typical QW and QDs but also certain intermediate state between QW and QDs was observed.
The sample grown on (911)B surface could be regarded as an example, which has a low
density of small QDs with weak PL emission and a strong WL signal with a life time
between the typical QW and WL of InAs QDs.

Finally, the evolution of InAs QDs formation was evident by the temperature dependence
of the PL measurements. Fig. 3 strengthened the physical picture with the integrated PL intensity as a function
of temperature. For sample B, the integrated intensity of its QD PL band started to
quench quickly after the temperature is higher than 160 K. This is a feature for InAs
QDs due to the strong 3D confinement, which demonstrates the ∼12 meV exciton binding
energy in these dots. Due to the fact that the excitons in the WL easily interacted
with the phonon and quenched, the integrated PL intensity of the WL of sample B began
to rapidly decrease as the temperature increased from 10 K. For the sample E with
only QW grown on (511)B, the PL started to fast quench from the temperature of 60
K due to the relatively lower binding energy of the excitons in QW. More interestingly,
we observed the temperature dependence behavior of the WL of sample C is between the
typical QW of sample E and the typical WL of InAs QDs on sample B, which confirms
that the sample grown on (911)B can be regarded as an intermediate state.

In summary, a clear evolution from QDs to QW was observed while the substrate varied
from GaAs (100) to GaAs (511)B. To our knowledge, it is the first time that such a
detailed evolution was observed by AFM, PL, and TRPL together. Since the growth condition
and the InAs deposition were identical for all of the samples, we attributed this
evolution due to the variation of the critical thickness on misoriented substrates.
As the substrate misorientation angle increased from 0° to 15.8°, our results indicated
a delayed formation of InAs QDs, which means an increased critical thickness. This
observation agrees with Sanguinetti’s reports, in which the critical thickness increased
as the substrate varied from GaAs (511)B to GaAs (311)B [20].

Generally, the formation of self-assembled InAs QDs is explained in terms of a thermal-equilibrium
picture where the system assumes the state of lowest free energy. The net energy of
a QD has been defined as [18,25]:

(a)

where Eelastic is the elastic energy relief due to partial strain relaxation inside the QD, Esurface is the surface energy associated with increased surface area of the QD, and Eedge is the energy associated with the various facets and the resulting edges of the QD.
During the SK growth of InAs QDs, the main driving force forming islands is the strain
relaxation, which permits relief of part of the strain induced by the lattice mismatch
between the epitaxial InAs layer and the GaAs substrate. As mentioned earlier, different
oriented substrate surfaces are characterized by different chemical potentials thus
affecting the kinetics of adsorption, migration, desorption, reconstruction, and strain
relaxation. In fact, the in-QD strain relaxation is influenced by the substrate orientation
and it has been proven that the strain relaxation is less efficient for islands grown
on high index surfaces [20]. For further evidence, the aspect ratio Q (height over width) for the samples was examined. The QDs grown on substrate with
larger misorientation angle appeared flatter and exhibited a lower aspect ratio (Q ∼ 0.09 on GaAs (911)B and Q ∼ 0.17 on GaAs (811)B) with the GaAs (100) case ( Q ∼ 0.18 for big QDs and Q ∼ 0.11 for small QDs ), which illustrate less strain relaxation for high index surfaces
[19]. The inhibition of strain relaxation inside the islands, by increasing the island
internal energy term, should determine a delay in the 3D growth mode onset. As experimentally
observed, the critical thickness increased as the substrate orientation departed from
the GaAs (100). It can be seen that our experimental results can be well explained
by the thermal-equilibrium model. The thermal-equilibrium model developed by Henini’s
group, not only work for the high indexed substrate with misorientation angle from
15.8° to 25.2°, but also work well for small misorientation of less than 15.8°. Therefore,
such a simple model in fact accounts for many experimental reports of strain-driven
island evolution on high indexed and/or vicinal substrates.

We also mentioned in the introduction that, our recent work of InAs QDs grown on patterned
substrates showed that the InAs QDs prefer to nucleate on the vicinal surface as compared
to the GaAs (100) surface [21,22]. In this case, it seems that the critical thickness of forming InAs QDs on the vicinal
surface is less than that on GaAs (100). However, the observations in this report
prove that critical thickness increased as the substrate orientation transitioned
from the GaAs (100). The developed thermal-equilibrium model by Henini’s group works
fine for the substrates with big or small misorientation angles. Therefore, we suppose
that in our previous investigation, the fact that the InAs QDs prefer to nucleate
on the vicinal surface is not due to the change of critical thickness, but due to
the increasing of effective deposition of InAs. Actually, many monolayer steps characterize
the vicinal surfaces. These ML steps blocked and trapped the In adatoms that migrated
from the nearby planar GaAs (100) surface, which caused an increase in the InAs local
coverage and make the real InAs deposition in the vicinal surface area reached the
critical thickness before the planar GaAs (100) plane. Therefore, the mechanism of
QD formation on the patterned substrate with vicinal surface is different for that
QD formation on the pure vicinal surfaces.

Conclusions

In conclusion, InAs quantum structures simultaneously grown on GaAs (100), GaAs (100)
with a 2° misorientation angle towards [01−1], and GaAs (n11)B (n = 9, 7, 5) substrates have been investigated by AFM characterization and PL measurements.
While the substrate misorientation angle increases from 0° to 15.8°, an evolution
from QDs to QW was clearly observed in both morphologic and optical investigations.
Interestingly, the sample grown on (911)B surface was observed as an intermediate
state between typical QW and QD structure, which has a low density of small QDs with
weak PL emission and a strong WL signal with a life time between the typical QW and
normal WL of InAs QDs. These observations show that the formation and the optical
properties of the quantum structures strongly depend on the substrate orientation.
The InAs QDs formation was delayed while the surface orientation departs from GaAs
(100), as they were reported previously on GaAs (311)B and GaAs (511)B. The evolution
from the QDs to QW was attributed to the less efficient of strain relaxation on misoriented
substrate surfaces. This report demonstrates, the thermal-equilibrium model developed
by Henini’s group, not only work for the high indexed substrate with misorientation
angles from 15.8° to 25.2°, but also work well for small misorientation of less than
15.8°. Therefore, such a simple model in fact accounts for many experimental reports
of strain-driven island evolution on high indexed and/or vicinal substrates.

Acknowledgment

The authors acknowledge the financial support of the NSF of US (through Grant No.
DMR-0520550).